Can I explode my mesh in Blender?
What you will do to start with is add a rigid body simulation to one of your objects and set it to active. You can do this in the Toolshelf, or in the Physics tab.



Then, in order to have the objects react to each other in close proximity. use the collision margin option. Adjust this to be as high as needed. The maximum is 1.0. If this needs to be animated, you can keyframe this as well.



Next, select all objects that compose the model being exploded, or rather that should share the same rigid body properties that you just made. I sometimes find it to be faster to take advantage of wireframe here to quickly select anything behind with border selection. Now, with everything selected go to the toolshelf>physics and select copy from active to copy the physics settings to all selected objects.   It is a good idea to remember to do this anytime you change the simulation or you may have an unexpected result.



After you have done this, head over to the scene properties, and you can bake the rigid body simulation. 





I just used a sphere after a cell fracture as an example, but this works with anything else also that is made of separate objects. You may also find it necessary to adjust the mass of objects in the rigid body settings.